‘fessing up – Number Talks gone awry

One of my professional goals this fall as a Math Liaison in my district is to spread the message of Number Talks far and wide in intermediate classrooms in my district.  Between the readings I have done (Making Number Talks Matter and Number Talks, blog posts, articles), the Pro-D workshops I have led (Number Talks book club, Number Talks and the Curricular Competencies, Intro to Number Talks), and the various Gr. 4-7 classrooms I have visited, I am starting to feel like a bit of an “expert” on the subject… and yet, Number Talks are still complicated and challenging.  I think that’s one of the things I like most about the Number Talks routine – it is simple enough to be accessible, but challenging enough to keep both students and teachers engaged.  So, today I thought I would share a blog post about a “failed” number talk that I have been pondering and what I learned from the experience.

The setup:

I was visiting a Grade 4 class – This was my third visit to this classroom this year, and I have done Number Talks with them on each visit.  We have done some dot talks and some addition number talks, and on this visit, we were going to be working on subtraction. Students in this particular class (and at this school in general) are very capable but tend to just do the traditional algorithm in their heads – this happens much more frequently here than at other schools that I visit (my theory is that it is related to high levels of parental involvement).

The Problems:

Rather than just one number talk, I brought a number string with me… My plan:

img_1745

I really thought that these (especially the first one) were going to be easy, but when we got going on the first question, I ended up with 4 different answers.  I have led a lot of number talks with multiple answers, and 99% of the time (100% of the time before this particular visit), the errors work themselves out nicely during the discussion of the problem.

So, for this particular problem, I got the following 4 answers:

img_1748
Take a minute and see if you can figure out where the errors come from.

I wish I had thought to take a photo of the board after we were finished (need to get better at documenting things for the blog!).  First, I had a few students who defended the correct answer of 6 with some good strategies – adding on, counting back, making 44 into 45 etc.  If I had taken a picture, you could note my nice use of number lines and whatever else I did to record student thinking…

But what I really want to discuss is the student who wanted to defend the answer of 14.

She said something like:

“I did the 5 minus the 4 to get 1 and the 4 minus the 0 to get 4.  The answer is 14.”

This is not really earth-shattering… probably the most common mistake made in subtraction by Grade 4 students.  Here is the interesting thing: this student had just listened to 3 or 4 of her peers defend (very clearly) their answer of 6 with very good strategies (and I’m quite sure she was listening).  This is the first time I have had a student sincerely defend a mistake after multiple other students have made their case for the right answer – she had no recognition that her answer might not be correct.  In hindsight, I can think of quite a few good ways to respond, but in the moment, I was caught off-guard.  I wish I could tell you that I referred her back to the original problem to see if her answer made sense… or that I asked a classmate to respond to her thinking… or that I asked her to explain why what she did made sense to her.  But… I just told her that you couldn’t flip the numbers around and subtract from bottom to top.  Sigh. Fail.

Even in the moment, I knew that my response was woefully inadequate… I could tell from the look on her face that I had done nothing to convince her.  I think she believed me that her answer was wrong, but she had gained no understanding to move her thinking forward.  Other students had not learned anything useful from our exchange.  And, possibly (hopefully not!), the experience has discouraged her from taking another risk to share her thinking.

Moving Forward

So, what have I taken away from this experience?  I went back to Making Number Talks Matter and reminded myself of some guiding principles…

  • Through our questions we seek to understand students’ thinking: It is not my role to be the judge of student answers, or even to correct mistakes.  It is my role to try to understand why students are thinking the way they are.  I need to focus my responses on questioning with the genuine desire to understand student thinking.
  • One of our most important goals is to help students develop social and mathematical agencyThis exchange would have been a great opportunity to encourage students to respond to each other.  By “explaining” the right answer, I removed the opportunity for students to be the thinkers and brought the responsibility for “correct mathematical knowledge” back to the teacher.  My new #1 goal for number talks: stop talking so much and LISTEN.
  • Confusion and struggle are natural, necessary, and even desirable parts of learning mathematics: In hindsight, it is really interesting how uncomfortable I felt dealing with this mistake… as teachers, it is very hard to let go of our instincts to help our students through their struggles.  I am totally on board with the IDEA of stepping back and letting my students wrestle with mistakes, but in the moment, it is still a challenge to stop the “traditional teacher” who hides out in the back of my brain.

I am thankful that teaching is such an interesting job – regardless of how much experience we have, there is always more to learn.

I am going to better prepare for my number talks… I have been lazy about anticipating student responses. For our last workshop, we prepared a “cheat sheet” of phrases and sentence stems, and I have printed a copy to refer to.

I am giving myself some grace… making mistakes is the best way to learn, even for teachers!

And I found this lovely quote from Ruth Parker to help me remember why I am so excited about doing Number Talks in the first place:

I’ve come to believe that my job is not to teach my students to see what I see.  My job is to teach them to see.

So… who else wants to ‘fess up?  What surprises have you been faced with during a Number Talk?

Number Talks Book Club

This fall, we (the two intermediate math liaisons in my district) have been planning a book study for the book “Making Number Talks Matter” by Cathy Humphreys and Ruth Parker. Our 18 participants teach Grades 4-7 and come from 16 different schools across our district (our district has 31 elementary schools).  We will be meeting every second Tuesday until the beginning of December to work our way through the book.  We will be talking about number talks, strategies for mental math and doing some planning and practicing of the Number Talks routine. Participation in this book club is totally voluntary and we know how difficult it is as teachers to squeeze in after-school commitments and still have everything ready in the classroom – our book club meetings run from 3:30 – 4:30 and we have committed to getting everyone out of there on time.

Yesterday was our first meeting – we had a few people who had to miss the first meeting because of parent-teacher interviews and staff meetings, so I will do my best to recap our discussion and learning!

We had a few goals for our first meeting –

  • Understand why we do number talks
  • Identify the procedures and setup necessary to get Number Talks started
  • Discuss the underlying values that the routine of Number Talks is based on
  • Create a plan for doing a dot talk in the classroom before the next meeting

We first showed the teachers a clip from the DVD that comes with Sherry Parrish’s Number Talks book.  We asked the teachers to ignore the mathematical strategies (for now) and just to focus on the routine – what is the teacher doing? What are the students doing?  What logistics do you notice?  (View this YouTube video from 44:50 to 51:30 – this isn’t the exact same clip we watched, but close enough).

Afterwards, we asked each group of teachers to fill in a chart with their ideas from watching the video and from doing the pre-reading.  Here are the finished ideas:

img_1702img_1703img_1704 

We then had teachers do a “gallery walk” to look at all the ideas.

Next, we had intended to pull up the new BC Curriculum website to show all the places that Number Talks fit in both the content elaborations and in the Curricular Competencies from Grades 4-7, but the website was down (*deep breath*), so we skipped this portion. We are planning to do a full workshop on our district’s next ProD day on Number Talks and the Curricular Competencies, so we will have a chance to dive into this further on that day (if you are from SD57 and reading this, you can register on PD Reg for this session!).

From here, we provided groups with some discussion questions from the chapters they read and gave them a few minutes to talk/discuss and plan:

  1. What strikes you as most useful/valuable/exciting about the Number Talks routine?
  2. What parts of the routine are of concern? What do you think will be most difficult for you as the teacher/facilitator?
  3. What norms and structures do you need to have in place to be successful with Number Talks?
  4. What Guiding Principles (from Chapter 3) resonate with you?
  5. Which ones make you feel uncomfortable/concerned?

We provided groups with a blank template to record some guiding principles/norms for Number Talks that they thought they might like to use in their classrooms.  There was so much good discussion during this portion of our meeting – I feel so lucky that I get to facilitate and work with groups of teachers on things like this – what a thoughtful group of people! During these conversations, teachers discussed the importance of “wait time” and how difficult that can be, they talked about the difficulties of facilitating if we ourselves are unsure about some of the strategies (hopefully we can clear some of these feelings up in future meetings), they talked about the importance of students listening to one another and how this routine can connect across many math content areas.

Finally, I did a demonstration “dot talk” so that teachers could see what a dot talk would look like in action.  I used the same dot pattern from the Chapter explanation and showed teachers briefly how I set up a number talk to get started.

For our next meeting in two weeks, we have asked teachers to try a dot talk (or several) in their classroom, and read Prelude to the Operations, Chapter 4 and Chapter 6 – we are going to dive into addition and subtraction number talks next.

Some resources:

These are the Guiding Principles that I use when I start Number Talks in a classroom – they are adapted from Making Number Talks Matter.

Here is a planning page that Dorianna and I made for a workshop we did last year on Number Talks (also adapted from Making Number Talks Matter).

I borrowed and adapted several ideas for this session from this blog – I am so thankful for teachers who share their ideas and work so graciously online!

This is a great summary of Number Talks if anyone is looking for more information.

Reading, reading and more reading

I had good intentions to blog this summer, but rest and family time ended up taking priority.  It’s October already!?!  So I am trying (again) to be committed to this blogging thing.

One thing I did manage to do this summer was some reading.  Professional reading is a bit of a wormhole.  One book leads to the next, which leads to the next and I always seem to have about 5 waiting for me to get to them.  This is what I managed to read this summer:

Essentialism: the Disciplined Pursuit of Less by Greg McKeown
This is the best productivity book I have ever encountered.  It is minimalism, but for your time instead of for your stuff.  I loved everything about this book, but a few things really resonated with me.

  1. It is impossible to do it all, so set some selective criteria that help to outline what you really want to accomplish and then STICK TO IT!
  2. Create a buffer by adding 50% to your estimate of how long it will take to accomplish things.  I am a chronic under-estimator of how much time things will take and often have to pull things together at the last minute.  I’m sure I would experience more EASE in my life if I consciously added in a buffer.
  3. Set aside professional time to think and read – this is really hard to do as a teacher – there are so many demands on our time.  But some of the most creative insights and solutions to problems come when I give my mind time and space to think.  I want to be intentional about adding this kind of time to my workweek this year.

The Innovator’s Mindset by George Couros
This book is related so closely to the shift our province is currently making in our curriculum – it is so much more important to teach our students HOW to think and learn rather than worrying about WHAT they are learning.  There is currently a MOOC going on as a book study with this book that I was trying to keep up with, but… I am about 2 weeks behind (see the comment about the buffer above).  Luckily, the Live chats are being archived, so I can follow at my own pace. (#IMMOOC if you are interested).

What’s Math Got to Do With It by Jo Boaler
I applied to read this book and write a review for the BC Association of Math Teachers book club series.  Jo Boaler’s books are so inspiring and her YouCubed website is full of great resources.  You can read my full review of the book here when it gets posted.

Classroom Chef by John Stevens and Matt Vaudry
I enjoyed the creativity of the lesson ideas and tips around crafting lessons.  I think many teachers feel anxious about straying too far from “predictable” in Math class and this book reminds us that there are rewards for doing so.  I actually (for the first time ever) thought it might be fun to teach a Grade 8 or 9 class.  Luckily, that feeling has passed quickly 🙂

Teach Like a Pirate by Dave Burgess
I am a couple of years behind the bandwagon on this one, but I have had it signed out of the district library a few times and have never made time to get through it.  I am glad I finally read it – there are so many great ideas for making lessons interesting and motivating for students.  This book was a good reminder of why I became a teacher in the first place.  A very motivating read!

And… that brings me to the present…

img_1692-1
I need to learn how to take non-blurry pictures with my phone… if I wasn’t so lazy, I would re-take this one.

Recently, I have been very intrigued by the idea of thinking routines and instructional routines that support deep thinking.  Making Thinking Visible caught my eye on Amazon and after ordering it, I am seeing references to it everywhere – a good sign.

I started Mathematical Mindsets in the spring and got about halfway through it – I really wanted to read it slowly and carefully because there is so much to think about.  I am looking forward to digging back in this fall.  This is the book I am considering for my next teacher book club – depending on how successful our Number Talks book club is this fall (more on this next week!).

So, that’s my professional reading life over the last while… does anyone have any good suggestions for what to read next?

 

 

 

 

 

 

Candy Math

As the end of the year approached, I was invited to bring some open-ended problem solving activities to a few classrooms.  A colleague that I met in a Math book study earlier this year had introduced me to 3 Act Math tasks and I thought it would be a perfect opportunity to try some.

I visited two Grade 4/5 classes and used Graham Fletcher’s Array-bow of Colours task.  One of my favourite things about my job as a math coach is that I frequently get the chance to teach the same lesson twice in a short time span – such a great opportunity for reflecting and thinking about my practice.

I began in both classes by asking students to Notice and Wonder about the Act 1 video. Here were some thoughts from the first class I was in:

Skittles S-Wood Noticing
This is why I love teaching… SUCH a huge variety of observations!  We had a chat about the difference between an observation and an estimation.  Some students were convinced that they actually counted 12 packages of skittles going in.
Skittles S-Wood Wondering
The kids came up with so many good questions!  I need to improve my photography skills…

We focussed on the “how many skittles” question for this activity, but I love the variety of questions they came up with and I love how many of them were actually measureable questions. I was pleased that someone came up with the question: “What if not every small pack has the same number of skittles?” I actually brought packages of skittles for the kids to work with (everything is more fun with candy) and I had debated how to handle this question, so I was happy that one of the students thought of it before we got started.  I was also so happy that it was a student who is typically not very engaged, and who doesn’t consider herself to be “good” at math.  It was a nice opportunity to really value her thinking!

We did some estimating and, as usual, had a HUGE variety of thoughts here.  You can see the range of the estimates in the first picture above – the lowest estimate in the class was 50 and the highest was 1050.

When we got to Act 2, the students knew they wanted to know the number of packages and number of skittles/package.  This class (and school) has a focus on multiplication as their essential skill for this year, so pretty much every group (partners) knew that they were going to multiply and no one had a hard time getting started.  Most groups quickly found the answer to 58 x 14 was 812.  The interesting challenge for this class was how they were going to address the variation in the packages.  As soon as students started opening their skittles, it became apparent that not every package was the same… 14 was the low end of the scale.  The highest number of skittles per package was 19 and most kids had something in between.  To account for this, some students added a constant at the end to account for there being “some” more skittles (ie. 812 + 50).  Some students changed their multiplication question – 58 x 16 (because 16 is between 14 and 19).  Some did two calculations – 58 x 14 and 58 x 19 and then picked a number in between.  This gave us opportunities for some rich discussions in Act 3.

I did the same activity with another 4/5 class the following day and noticed some interesting differences.  The second class was in an inner city school and they have not had the focus on multiplication as an essential skill.  They generally struggled a lot more with this activity, but still had some good observations and ideas.  Their estimates were wildly off – the range for the class was between 100 and 400.  Overall, they knew they were going to multiply, but didn’t have the skills to do the 2×2 digit multiplication.  They were much more confused about the variation in number of skittles/package.  In hindsight, knowing that they were less comfortable with multiplication, I might have waited to hand out the skittles packages until the end and then we could have had a whole-class discussion about what to do with the variation in package size.  I think this would have filtered out some of their confusion during act 3 – some students were really quite paralyzed by the variation in packages.  I still think this activity was valuable for them.

One of the things I like about this particular task is the photo provided for Act 3.  This gave us a neat little opportunity to talk about efficient ways of counting/grouping – it made for a good visual number talk at the end of the task.

I also recently visited a Grade 6/7 class and I used Dan Meyer’s “Super-Bear” task.  The kids were really engaged (which is quite impressive for this particular class) and all groups ended up with a workable strategy.  If I were going to do this again, I would encourage the use of calculators – most lots of groups just got bogged down in a problem that required long division with decimals (this is understandable… I’m pretty sure I would get bogged down tackling a long division with decimals problem too).  I think the value in this activity is in the problem-solving nature and not in the calculation piece.

My takeaways:

  • I am eager to try out some more 3 Act Math.
  • I love that they are such an engaging way to have kids problem solve.
  • I enjoy giving the responsibility for all the thinking to the students… these tasks really make me feel like I am a facilitator rather than a teacher.
  • I am really going to encourage teachers and schools next year to pick a topic or idea to really focus on in their Math instruction.  I have been so impressed by the school that I have been working in that has really narrowed down their approach and really worked collaboratively to ensure that students progress.
  • There are so many of these tasks available online and for such a wide range of grades and topics -I am so grateful to all the teachers who have spent time developing these and sharing so generously online!

If you are new to 3 Act Math tasks, I would highly recommend this video by Dan Meyer in which he demonstrates the implementation.

Happy summer to any other teachers out there who had their last day today!!

 

Noticing and Wondering Across the Grades

I have been reading a lot lately about having kids “notice and wonder” to start off a math task.  This seemed to be a nice extension from the Number Talks that I have been doing lately, so I was looking for an opportunity to visit some classes to try it out.  Then, last week, a friend of mine posted this picture to her Facebook page…

Egg Array
An egg array – beautiful!

… and I knew I had to use it!  There are sooo many awesome things to notice and wonder about in this picture!

 

So, I “invited” myself into some classrooms at my school.  I was especially curious about how kids at different grades would respond similarly/differently to this photo.  I visited a Grade 1/2, a Grade 2/3 and a Grade 3 class with the same activity.  First, I showed the whole class the picture and gave them a few minutes to observe and think about what they noticed and wondered.  Then, I collected all their ideas onto the whiteboards at the front.  I was so impressed!  I love how curious kids are at this age, and I love the variety of things that they noticed and wondered about:

P1000152
Grade 1/2 noticings and wonderings – lots of math “noticing” already
Branigan
Grade 2/3 noticing and wondering
Dunn-notice
Grade 3 noticing (I JUST realized that I put a “wonder” in the “notice” list – oops!)
Dunn
Grade 3 wonderings

I love how many things the Grade 3’s wondered about before they wondered how many eggs there were! I think my favourite “noticing” is “it looks like they just came out of a chicken!” And I love how much real-world knowledge is being talked about here – in addition to the math.  I thought it was so interesting to hear the variety of background knowledge that the kids had about chickens, farms, eggs, and where their food comes from.  They were all very enthralled by that tiny egg in the middle (which, by the way, had no yolk according to my “farmer” friend).

Next, we did some “math” with the picture.  I gave all the kids a black and white copy of the picture in a sheet protector and a dry erase marker to use.  I challenged them to figure out how many eggs were in the picture WITHOUT counting one-by-one.

Here are some samples from the 1/2 class…

Grade 12-3
Grade 1/2 sample – I have never taught these grades, so wasn’t sure how easily kids would be able to count by grouping.  I was expecting to see a lot of this, but only had a few that ended up counting one-by-one.
Grade 12-4
Grade 1/2 – A slightly more sophisticated version of one-by-one counting.
Grade 12-1
Grade 1/2 – interesting! This student started counting by 2’s but got to 22 and couldn’t continue, so she switched to counting by 1’s to finish off.

 

Grade 12-2
Grade 1/2 – counting by 3’s, but a little mix-up at the end.  This reminds me of a hundreds-chart layout for counting by 3’s (row-by-row).
Grade 12-5
Grade 1/2 – this was the most sophisticated version from the 1/2 class.  It looks like he counted 1 by 1 but when I asked him about his picture, he explained that he did 9 groups of 4.  I like how he arranged it as a grid.

And a few from the 2/3 class…

Grade 23-1
Grade 2/3: Counting by 3’s
Grade 23-5
Grade 2/3: Counting by 4’s

 

Grade 23-3
Grade 2/3: Counting by 4’s a different way
Grade 23-4
Grade 2/3: Counting by 6’s
Grade 23-2
Grade 2/3: Hmmm… interesting.  I’m just guessing here, but maybe the student decided that counting by 2’s would take too long?  In any case, this is probably the most unique grouping I saw!

With the Grade 2/3’s we ended up discussing that 36 is a really interesting number because there are a lot of ways that you can group the eggs and still get to 36.  We talked about the word factor and how we could use it to describe the way we grouped the eggs (ie. my picture shows 9 groups of 4 – 9 and 4 are factors of 36).

And the Grade 3’s:

Grade 3-3
Grade 3: Counting by 3’s – an interesting way of grouping
Grade 3-1
Grade 3: This student actually grouped them a few different ways.  He counted by 2’s and then by 3’s and then had a great idea: “I bet I can put them in dozens!” Kind of a cool connection to real-life knowledge about how we buy eggs.

So… after all that… what did I notice and wonder?

I noticed that the kids were all really engaged in this activity.
I noticed that all the students (even the lowest Grade 1/2’s) were able to meaningfully engage with this activity.
I noticed that many kids wanted to try different ways of grouping and were getting ideas to try from their neighbours.
I noticed that all the students were keen to explain their thinking.

AND… I noticed… that not ONE student in any of the classes grouped the eggs in a “traditional” array pattern.  There were some kids who counted by 4’s, but none made columns of 4.  And nobody thought to make rows of 9 or to turn the page and make columns of 9.  This is a big ??? for me, because I would think it would be natural to group things in rows and columns, and this is where we want kids to access multiplication.  So, this leaves me wondering… do the students naturally group things the way that they did because of experience using hundreds charts?  What kinds of activities can we do to help them see things in arrays?  Should I be “encouraging” kids to see an image like this as an array, or will that representation naturally develop over time?

So much to think about!!  I love activities that make me wonder about my teaching and student learning.  I will definitely be doing more noticing/wondering with kids…

If you are interested in doing activities like this one with your students, there are many more images like these available on the Number Talk Images website and I have submitted the picture from this activity there as well.

 

 

Number Lines + Fractions

As a grade 4/5 teacher for the last 4 years, I generally find that my students enjoy working with fractions.  They like working with fraction manipulatives and approach visual representations for fractions with relative ease.  Naming and identifying fractions is rarely a problem.  But then we get to comparing and ordering fractions… and it all falls apart.

With my tutoring students (Grades 9-11), fractions are generally a disaster.  They are chugging along fine with whatever they are working on and then… a FRACTION!!!  Reducing fractions and finding common denominators is sometimes OK, but if a fraction is tossed into the middle of an algebraic expression, they don’t know what to do.  There seems to be no recognition that fractions are, in fact, numbers.

I have been doing a lot of thinking this year about how and why fractions seem to be a place of struggle for so many students as they advance through math.

Many of my students treat fractions as a completely new set of numbers, with no connection to whole numbers.  They are obviously not getting the big idea that all numbers are connected and have their own place on the number line.  Part of me wonders if this is because we (I?) over-use certain representations for fractions (pizzas and chocolate bars) and under-use others (number lines).  So, this year, I have really been trying to help students connect what they already know about numbers with the new information that they are learning about fractions.

One activity that I have used a few times this year – very successfully – is a fraction clothesline activity.  This week, I was invited to visit a Grade 4/5 class to introduce decimals by linking them to what the students already knew about fractions (they have been working on fractions for a couple of weeks).  I thought this was a perfect opportunity for me to combine two great things and I set the fraction clothesline up like a number talk (yes, I am obsessed with Number Talks).

I set up the clothesline at the front and we looked at the three benchmark cards I brought: 0, 1/2 and 1.  We hung the 0 and the 1 on the number line and then… NO ONE could tell me where 1/2 went.  Yikes.  This is the part of number talks that still makes me anxious… the WAITING… letting kids think… and HOPING… that SOMEONE… will come up with something to move the conversation forward.  My patience paid off… eventually someone suggested – “well, if it’s one-half, couldn’t we just put it in the middle?”  And, whew… yes.  Yes, we can.  We were rolling again.

Fraction Benchmarks

So, once we had the benchmarks on the line, I handed out a fraction card to each student.  Because we were looking at connecting decimals and fractions, I gave each student a “tenth” – nothing tricky.  Just 1/10 – 9/10.  I asked the students to think for a moment and give me a thumbs up when they were pretty sure they knew where their fraction was supposed to go.  And I waited.  After a while, a few kids (probably about 1/2) had their thumbs up.  So I invited those students who had an idea to come and place their fractions, and others could just watch to see if it helped them figure out where theirs should go.  And… this is what I got:

Fraction Number Line
This photo is actually a re-enactment… I need to get better at taking photos as I go.

Yikes.  Again.  But mistakes are SUCH a valuable opportunity to pinpoint misconceptions. The first student started by defending the location of 9/10.  He explained that because 9/10 was almost one whole, he put it close to the 1.  Whew.  Good start.

Then, the student who placed 1/10 wanted to explain.  She said she placed her fraction there because 10 is bigger than 2, so 1/10 must be bigger than 1/2.  Cool – good explanation, and a good misconception to tackle.  But, this is where I am still working on my “thinking-on-the-spot” skills, and trying to find the balance between “teaching” and letting the students help each other and wrestle with their own thinking.  I ended up drawing some pictures on the whiteboard behind the number line – I went back to the classic “pizza” shape.  I asked the students to help me draw 1/2 behind the 1/2 benchmark card and then 1/10 behind the 1/10 card.  Gasps all over the classroom.  I asked the student if she was still happy with where her card was and – NO, she was not!  She came and moved it to its correct location.  I asked if any other students wanted to move theirs and several more came up to make adjustments (accurately).  I asked the students to explain why they chose to move their cards and they were able to relate the spot on the number line with what the picture would look like.

I then encouraged the students who had not yet placed their cards to come up and find a reasonable spot for them.  This worked well – most of them were able to be successful in the location and were able to explain why.  We also talked about the spacing between fractions on the number line and how it is hard on a clothesline to be exact, but we know that fraction pieces all have to be the same size.

I was pretty happy with this number talk.  The students were pretty confident with ordering fractions with the same denominator, and I thought we got a good start at thinking about fractions with different denominators.  At the end, I gave a few students some “tricky” cards – 0/10, 11/10 and 12/10 and they were able to successfully place and explain these fractions as well.

This lesson really highlighted (again) for me the power of number talks and having opportunities for students to own and explain their thinking.  The real power of number talks is in giving students these types of opportunities on a DAILY basis.  This is what helps them to build up their number sense over time.

What other activities do you use to help students build a broad, connected understanding of fraction concepts?